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Beliebt Rechnen >

integral of 1/(x-2x^2)

Lösung

\int \frac{1}{x - 2 x ^{2}} d x

Lösung

ln ∣ x ∣ - ln ∣ 2 x - 1 ∣ + C

Schritte zur Lösung

\int \frac{1}{x - 2 x ^{2}} d x

Ermittle den Partialbruch von

\frac{1}{x - 2 x ^{2}} : \frac{1}{x} - \frac{2}{2 x - 1}

= \int \frac{1}{x} - \frac{2}{2 x - 1} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{1}{x} d x - \int \frac{2}{2 x - 1} d x

\int \frac{1}{x} d x = ln ∣ x ∣

\int \frac{2}{2 x - 1} d x = ln ∣ 2 x - 1 ∣

= ln ∣ x ∣ - ln ∣ 2 x - 1 ∣

Füge eine Konstante zur Lösung hinzu

= ln ∣ x ∣ - ln ∣ 2 x - 1 ∣ + C

Graph

Beliebte Beispiele

integral of (2x)/(5+3x^2)

\int \frac{2 x}{5 + 3 x ^{2}} d x

integral of (8+t+6t^2-12t^3)/((3t^2+4)(t^2+7))

\int \frac{8 + t + 6 t ^{2} - 12 t ^{3}}{( 3 t ^{2} + 4 ) ( t ^{2} + 7 )} d t

integral of 1/(x^4(x^2+1))

\int \frac{1}{x ^{4} ( x ^{2} + 1 )} d x

integral of (x^2)/(sqrt(x^2+100))

\int \frac{x ^{2}}{x ^{2} + 100} d x

integral of xe^{-kx}

\int x e^{- k x} d x